Two triangles ABC and DBC lie on the same side of the base BC. From a point P on BC, PQ $∥$ AB and PR $∥$ BD are drawn.They intersect AC at Q and DC at R, respectively.
Prove that QR $∥$ AD.

Open in App

Solution

Given : PQ $∥$ AB and PR $∥$ BD.

$PQ ∥ AB . Therefore, according to the basic proportionality theorem, \frac{CQ}{QA} = \frac{CP}{PB} . . . . (1) PR ∥ BD . Therefore, according to the basic proportionality theorem, \frac{CP}{PB} = \frac{CR}{RD} . . . (2) From (1) & (2), we get: \frac{CQ}{QA} = \frac{CR}{RD} Therefore, according to the converse of basic proportinality constant, QR ∥ AD .$

Suggest Corrections

Similar questions

Q. Two triangles ABC and DBC lie on the same side of the base BC. From a point P on BC, PQ||AB and PR||BD are drawn. They meet AC in Q and DC in R respectively. Prove that QR||AD.

Q. ∆ABC and ∆DBC lie on the same side of BC, as shown in the figure. From a point P on BC, PQ ∥ AB and PR ∥ BD are drawn, meeting AC at Q and CD at R, respectively. Prove that QR ∥ AD.

$Δ A B C$ and $Δ D B C$ lie on the same side of BC, as shown in the figure. From a point P on BC, PQ || AB and PR || BD are drawn, meeting AC at Q and CD at R respectively. Prove that QR || AD.

Q. In the given figure , two triangles ABC and DBC lie on the same base BC . P is a point on BC such PQ || BA and PR || BD . Prove that QR || AD .

Q. Question 8
ABC and DBC are two triangles on the same base BC such that A and D lie on the opposite sides of BC, AB = AC and DB = DC. Show that AD is the perpendicular bisector of BC.

Join BYJU'S Learning Program

Two triangles ABC and DBC lie on the same side of the base BC. From a point P on BC, PQ∥AB and PR∥BD are drawn.They intersect AC at Q and DC at R, respectively. Prove that QR ∥AD.

Two triangles ABC and DBC lie on the same side of the base BC. From a point P on BC, PQ $∥$ AB and PR $∥$ BD are drawn.They intersect AC at Q and DC at R, respectively.
Prove that QR $∥$ AD.